Question

The diagram represents a rectangular garden of length 13 m and width 10 m.

The flower beds are triangles and the patio is a trapezium.
The rest of the garden is lawn.
6m
10m
Patio
4m
Not to scale
Lawn
6m
2m
Flower
bed
Flower
bed
5m
Work out the area, in m², of the lawn.
+
[6]

Answer 1

To work out the area of the lawn, we need to subtract the areas of the flower beds and the patio from the total area of the rectangular garden. We can do this as follows:

Calculate the area of the rectangular garden:

Area of rectangle = length x width = 13 m x 10 m = 130 m²

Calculate the area of the flower beds:

Area of triangle 1 = 0.5 x base x height = 0.5 x 6 m x 4 m = 12 m²

Area of triangle 2 = 0.5 x base x height = 0.5 x 5 m x 2 m = 5 m²

Total area of flower beds = 12 m² + 5 m² = 17 m²

Calculate the area of the patio:

Area of trapezium = 0.5 x (base1 + base2) x height = 0.5 x (6 m + 10 m) x 4 m = 32 m²

Subtract the areas of the flower beds and patio from the area of the rectangular garden to get the area of the lawn:

Area of lawn = Area of rectangle - Total area of flower beds - Area of patio

Area of lawn = 130 m² - 17 m² - 32 m²

Area of lawn = 81 m²

Therefore, the area of the lawn is 81 m²

Explanation:

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